Sophia Loren, Charlie Chaplin and Robert De Niro are flashing past in a disorientating whirl. My elevator is hurtling up the centre of Italy's National Museum of Cinema, whizzing past a gallery of movie posters and stills, up to the pinnacle of the domed roof. I step out of the lift and on to the viewing platform at the highest point in Turin.

This building, Mole Antonelliana, is Turin's landmark, the tallest brick building in Europe. It was designed as a synagogue in the 19th century, but took so long to build that the city's Jewish community got fed up and decided to build their place of worship somewhere else.

Movie buffs will love the museum's brilliant collection of posters and other memorabilia, including props from films ranging from Cecil B DeMille's The Ten Commandments to Star Wars, the alien from Aliens, Federico Fellini's sketches and the original script from Godfather Part II. The museum recreates the exhilaration of cinema at its best - you don't know what will happen next. The rooms, once intended to be chapels, each have a theme - now you're in a 30s family sitting room, now you're in a giant fridge sitting on a toilet; now you're in a pharaoh's tomb. On the floor are reclining seats from which you can view movie clips with the building itself as the star, the domed roof becoming a giant magic lantern.

Turin was the centre of Italy's film industry from the days of the Lumière brothers until Mussolini, who hated anti-fascist Turin and moved it lock, stock and barrel to Rome. The city has also been used for numerous locations, including The Italian Job, where Michael Caine and his Minis race round the rooftop test track at the Fiat factory.

Built in 1920, the enormous Fiat factory (Il Lingotto), with its sleek lines in cream, green and black, is a modernist masterpiece. The building itself was a machine - the cars would be pushed upwards floor-by-floor during each stage of assembly, until the finished models arrived on the roof (La Pista) for a test drive.

Fiat (Fabbrica Italiana di Automobili Torino), like much else of note in Turin, was owned by the late Gianni Agnelli, deemed the most powerful man in Italy.

Il Lingotto has been remodelled by the architect Renzo Piano into a hotel and leisure complex, but it is possible to get your taxi driver to take you up the building's spiral driveway until you are on La Pista, still gorgeous and immaculate, and now home to a divine restaurant. I enjoyed a heavenly risotto with the local castelmagno cheese; the sweets are served on a chunk of vintage Fiat engine.

After lunch we took a stroll across the magnificent roof to a gallery showcasing the Angelli family art collection. The Pinacoteca Giovanni e Marella Agnelli displays a mere 18 pieces, but they include masterpieces by Canaletto, Renoir, Gauguin, Picasso, Matisse and appropriately, Italian futurist Gino Severini, who like the Agnellis, glorified machines.

Central Turin itself is an architectural wonder: built in the baroque style, with harmony and order paramount - unlike the anarchy of other Italian cities. Seventeen kilometres of the city is laid out symmetrically with porticoed pavements, the covered walkways offering shade and archways offering a degree of intimacy. But it's a proper city. Nietzsche, a former resident, loved Turin because it seemed to have "no nasty suburbs".

He was wrong about that, as with so much else, but it's easy to imagine that Turin consists solely of its central quarters. Walking around the city centre, one is suddenly confronted, down a boulevard, with the Alps, looming from behind the heat haze. Turin hosts the winter Olympics in 2006, its proximity to some of Europe's best ski resorts making it an obvious choice.

And like any great city, it has a great market. The vast Porta Palazzo is like a cross between Brick Lane and Portobello Road - a multicultural mishmash of aromas and styles in its food and clothing markets, but with a rather more genteel antiques area (known as Balon).

After the open-air shopping, time for a spot of alfresco dining at the modish Cafe Torrino, where meat and fish are served raw, and you cook it yourself on your very own chunk of white-hot volcanic rock.

Turin, and the surrounding province of Piemont, play an important part in Italy's world-beating gastronomic reputation. It is here that the Slow Food movement was founded in resistance to, well, fast food. Each meal I had here was exquisite, as was the wine, a good local choice being Barotto, known as "king of wines, wine of kings". Turin is also famous for its chocolate - Ferrero Rocher is made here, and the city styles itself the "capital of chocolate". But it could make a similar claim for its coffee. The Lavazza empire began here 100 years ago, when Luigi Lavazza started a grocer's shop at San Tommaso 10, now a superb restaurant with a special menu for different Lavazza coffees.

Fully re-caffeinated after Caffe Lavazza, we sampled a few lively bars in the buzzing Roman Quarter, before hopping in a cab a short ride back to the jaw-droppingly stylish Hotel Boston, mercifully situated in the quieter Crocetta district.

What with all the shopping and eating, and gawping at the buildings, it just wasn't possible to see absolutely every art treasure in the city. Leonardo's self-portrait in the Royal Armoury, one of Europe's finest Egyptian museums and the city's 28BC Roman gate in the 15th-century Palazzo Madama will have to wait for a future visit.

I did, however, spend a pleasant couple of hours in the Gam art gallery (Galleria Civica d'Arte Moderna e Contemporanea), with its impressive collection of 19th and 20th century art. Even better, a half-hour's drive from Turin, is the castle town of Rivoli, where the former chateau has been converted into a contemporary art gallery. Great food was not far away: the castle also boasts a restaurant with a Michelin star.

The Castello di Rivoli contains works by Bruce Nauman, Richard Long, Henry Moore, Gilbert and George and a number of Italian artists new to me, including Maurizio Cattelan, who created a carpet basted on the Formaggio Bel Paese box design, a lifesize dummy of a schoolboy stuck to his desk by pencils jabbed through his hands, and a stuffed horse suspended from the ceiling. Nice.

But there were enough surreal touches back in town. Behind the central Piazza della Repubblica, is the Santuario della Consolata, Turin's most elaborate church. As moving as any artwork I saw during my stay there was a series of paintings known as "the sorrows", in which parishioners depict various life-threatening scenarios from which they have been saved. These include sinking ships, collapsing buildings, bombs, charging bulls, disease, exploding chip pans, and (a personal favourite) cutting electric cables with garden shears.

Antonello, the same architect of the synagogue that never was, provided another extraordinary sight in the centre of town: he designed a thin, yellow house based on a slice of polenta, Fetta di Polenta. Which is making me hungry ...

Great food, unique designs, but the people of Turin, with their Calvinist, rationalist traditions, eschew the flash of Milan and the operatic drama of the Rome. An attitude that appeals to us reserved Englishmen. But even though it's got a cultural life the equal of any great European city, there aren't many tourists there. Which also suits me fine.

Way to go

British Airways (0870 850 9850) flies from London Gatwick to Turin from £49 excluding taxes. The price is subject to availability.